Jazz Science

Sunday, February 8, 2015

It's very common in jazz education to encourage a chord-oriented perspective on improvisation. In many ways, this makes a lot of sense and can be a valuable way of analyzing the music. However, it runs the risk of one failing to see the forest for the trees when applied to many tonal jazz standards, where a key-oriented approach provides a better perspective of how everything really fits together. It can also lead to more lyrical, melodic lines that can provide a contrast to lines that outline the chord changes more. Ultimately, I think both perspectives have their place. Obviously, in tunes that are less tonal, the key-center perspective becomes much less useful.

I was thinking about this today and thought it would be interesting to look at the diatonic chords in a key, and compare what notes in the key worked where, to get a global view of the relationships. The results are interesting, I think:

Green: worksOrange: mildly dissonantRed: strong dissonance

What is interesting here is how nearly every note in the key "works" against nearly every chord. In particular, that scale degrees 2, 3, 5, and 6 can be used anywhere. Note that this is 4/5 of the major pentatonic scale. The 7th degree works nearly everywhere (and even the dissonance against the ii chord is fairly mild). If you take 5, 6, 7, 2, 3, then you have the major pentatonic on the 5th degree as being a pretty much failsafe option against any diatonic chord.

Also interesting:

• Nothing conflicts with the IV chord (this is just the scale-oriented version of the observation from the standard chord-oriented perspective that the Lydian mode has no "avoid" note).

• The 1st and 4th degrees are the only ones that are seriously problematic. The first degree clashes with the dominant functioning chords (V and vii°) and the 4th degree clashes with the tonic-functioning chords (I and iii, and to a lesser extent, vi).

While I do not advocate mindlessly improvising according to general rules, I do think it is interesting and perhaps helpful to be aware of the relationships in the big picture. And of course "works" and "doesn't work" is a extremely simplistic framework for understanding relationships, one could conceivably do a much more nuanced chart of how every scale degree and chord relate to one another (and I think that every accomplished improviser does have a personal sense of this, whether or not it is conscious or articulated).

For instance, a very slightly more nuanced chart might be:

Same as above, but add:Yellow: subtle tension

The fourth degree on a minor chord has a slight tension to it in normal tonal progressions, so one could further refine the chart with this information. This is moving us a bit in the direction of a chord-oriented approach. However personally useful this is, it does make the big picture less clear, which is what I meant earlier about missing the forest for the trees.

Then I thought, what about common chromatic chords? So I made the following chart:

Obviously quite a bit more red here, as one might expect in restricting melody choices to diatonic scale degrees while adding in chromatic chords: at least one note in each chord is outside the key.

Here are my observations:

• The tonic works against all of these common chromatic chords.

• II7, III7 and VI7 only have one conflict, the 4th of each chord (2, 5, and 6, respectively). This results in an interesting tetrachord that will work over all three: 1 3 4 7 (the two diatonic half-step pairs). Although a chord-oriented approach also advises against the 4th degree on a dominant chord, it is interesting to analyze these three dominants according to a chord-oriented approach to observe the differences: II7 (7, 1, 9, +9, 4, 5, 13), III7 (b13/+5, 7, 1, b9, +9, 4, 5), VI7 (+9, 4, 5, b13/+5, 7, 1, 9)—using notes from the key actually encourages the use of altered 9ths and 13ths with respect to the chordal harmony.

• bVII7, a common chord in bebop, works great with the first 5 degrees of the scale (and results in 3, 5, 9, #11, 13 against the chord).

• #iv diminished 7, a troubling chord for a lot of students, works great with the simple 1 2 4 6 7 (rearranged as 6 1 4 7 2 it becomes 3, b5, 7, 11, b13 relative to the chord)

One of the things that comes from adopting the perspective is that you start to see the key as stable, and the chords as merely temporary events that are happening in the context of the key. While it's important to be able to zero in on the notes that change (i.e., playing the "changes") it's also effective to emphasize the stable notes that aren't changing. The simple fact that the 5th degree works over every diatonic chord, for example, could be used as a unifying central element in an improvisation using many other elements.

I frequently make the observation that any note in a piece of music is simultaneously functioning with respect to the key and with respect to the current chord. That means that a chord can be stable/tense on two different levels at any given time, and they can agree or conflict (there are 4 different possibilities, obviously with many subtle gradations: key stable/chord stable, key stable/chord tense, key tense/chord stable, key tense/chord tense). It can be valuable to consider both ways that any note is working. Here is a chart with a few examples of how things can line up. In this case, I think it is helpful to consider more subtle shadings of tension, so here I only included unambiguous cases:

Note that any note that is chromatic to the key would be fairly tense—this is an issue often that confuses students when they are told things like "natural 9 is consonant on a diminished chord", which is true (chord-stable), but in many key contexts, the natural 9 of the dim. chord is extremely key-tense. For example, the common #iv°7 would have #5 of the key, a very tense note, as the 9. It's not unusable, but it requires extra care to use it musically. Each particular combination of notes/chords is different, but you can see that there would be at least 3 basic categories of tension: stable (key-stable/chord-stable), mixed tension (key-stable/chord-tense, key-tense/chord-stable) and very tense (key-tense, chord-tense).

For a practical exercise that has some relationship to all this analysis, see the following post:

This isn't really a methodical theory approach as much as it is just some thoughts and observations that I thought might be helpful. I'll be curious to hear any thoughts you might have in response to these ideas.

Tuesday, March 27, 2012

Here are more rootless voicings for guitar, based on the "Bill Evans" left-hand style voicings.

These are mostly drop-2 chords, so unlike Evans's close voicings, these are open voicings. This does change the character of the sonority considerably; if the aspect of Evans's voicings that you want to imitate is the crunch of the 2nd, then the close voicings in the previous post or 3-note voicings would be more appropriate. That consideration aside, these are very useful and hip-sounding voicings.

Perhaps I'll deal with a 3-note voicing approach in some future post.

Again, I've arranged these in the context of a II V I progression to clarify the voice leading and usage.
See my notes from the previous post for more details.

These are all on the 1234 string set, but most of these can be translated to the 2345 string set. You can do this yourself (it's a great way to learn), or wait a few days and I'll post the 2345 voicings.

Bill Evans Rootless Guitar voicings, 1234 string set, page1

Bill Evans Rootless Guitar voicings, 1234 string set, page 2

Bill Evans Rootless Guitar voicings, 1234 string set, page 3

At this point, you may be wondering about the directive that the voicings must have either the 3rd or 7th (or 6th) on the bottom.

The main reason for this is that without the root motion, the 3rds and 7ths provide the clearest definition of the chord sound; having them on the bottom just makes it sound stronger. However, the reality is that you may sometimes prefer to voice another note on the bottom; the alternatives obviously are 1 (or 9) and 5 (or 6).

Interestingly, if you alternate all 3rds and 7ths, or all roots and 5ths, you end up with smooth descending voice leading through circle of 5ths progressions.
If instead, you mix them, you can create interesting contours, some ascending and others descending.
For instance, 3579 to 1367 to 5793 to 3579 creates a general upward movement instead of downward.

Also, when comping, the general downward trend of tonal voice-leading means you eventually either run out of fretboard (or keyboard), or you have to break the voice-leading by leaping upward occasionally. There are a few ways to smooth this out.

One is to make the leaps after cadences, where they are less disruptive (e.g., ii7 V7 I VI7, you leap to the VI7, not to the V7 or I, so that the cadence has smooth voice-leading).

The other is to make judicious use of inversions that lead upward once in a while—for this, the voicings with the 1, 9 or 5 on the bottom are most useful.

I suggest mastering a substantial portion of the voicings with the 3rd and 7th on the bottom before messing with the others.

Sunday, March 25, 2012

The uses of triads for an improviser are nearly limitless. As I hinted at in my previous post on digital patterns, adding a note to a triad to create a four-note group can create a lot of possibilities. The standard digital patterns 1235, 1345, and 1356 are all examples of a triad with an added note (1356 and 1357 can also be considered arpeggios).

I'm working on putting a whole book together of various ways of incorporating triads into your playing. Here's an excerpt from the section on added-note triads. I indicate the scales in which the pattern can be found, as well as the main harmonies over which it can be used. Of course, these can be used with substitutions as well, and with more 'outside' playing to break out of the strict harmony.

I indicate the pattern with either a capital or small "m" for major or minor triad, "A" for augmented, "d" for diminished, with the interval from the root of the triad (using +/- to indicate a sharpened or flattened degree. For example, M-2 = Major, with added b2.

There are a lot of ways to practice incorporating these ideas. The first thing I would suggest is getting familiar with all the inversions and permutations. Then pick a simple chord progression like "Autumn Leaves" and figure out all the places where various transpositions can be used.

Here is a set of rootless voicings for guitar that I adapted from the stock "Bill Evans" style left-hand voicings. I show them in a II V I context to illustrate the voice leading, but they can of course be adapted to fit any chord progression.

Close voicings tend to be difficult on the guitar, as they contain smaller intervals. Many of these involve challenging, but not impractical stretches: they should be usable by most guitarists, unless you have rather small hands. When practicing these, make sure you are warmed up first, well-hydrated, and take frequent breaks, as it is easy to overdo it when practicing these kinds of stretches and you want to avoid injury.

For those unfamiliar with the principles of the "Bill Evans" style voicings, here are the main principles:

• They are generally voiced with either the 3rd or 7th on the bottom

• The basic structures are 3715 or 7135—note that the chord can contain the root, they are just "rootless" in the sense that the root is not in the bass

• On m7 chords, the root may be replaced with the 9th, and the 5th may be replaced with the 11th

• On 7 chords, the root may be replaced with the 9th, and the 5th may be replaced with the 13th or #11 if appropriate

• On Maj7 chords, the root may be replaced with the 9th, the 5th or 7th may be replaced with the 6th

• One m(maj7) chords, the root may be replaced by the 9th, the 5th or 7th may be replaced with the 6th

• In circle of 5ths motion, alternating voicings with 3 and 7 on the bottom will create smooth voice leading.

Of course, the 9ths on the 7 chords can be altered as well, and #11s can replace 5ths in the maj7 chords also when appropriate. I also bent the "rules" in a couple of cases because of guitar limitations.

On the following pages, the chords are presented in columns. Any chord in the II column can lead to any chord in the V column, which can in turn lead to any chord in the I column.

This isn't to say that all combinations work equally well or in all cases. For example, using a m13(maj7) chord when the chord in the tune is Maj7 will probably not work so great (but don't let me stop you!).

Here are the voicings where the II chord has the 3rd on the bottom. Because of the 2nd between 7-1 and 9-3 that occurs on the II and I chord when you start with the 7th on the bottom, there are not many practical voicings on guitar that way. There are some, however, and I'll post them soon along with the drop-2 versions of the chords and some tips on how to get creative with them while comping.

Wednesday, March 21, 2012

Okay, I haven't posted in a year. Here's a little worksheet of common patterns that are often used by modern improvisers. John Coltrane was probably the first to make notable use of these kinds of patterns, which he did on the record "Giant Steps".

I took the basic patterns and explored the possibilities for reordering the notes and for octave displacement.

There are 24 different ways to order four notes, these are all listed for each type.
If you add in octave displacement of various notes, you end up a lot more variations. I just did the first example from each chord type . . . you can work out the rest.

You can use these starting on different chord degrees, the first page lists some possibilities:
• Use the major pattern from the root or 5th of a maj7 chord, or from the 3rd or 7th of a min7 chord
• Use the minor pattern from the 3rd or 6th of a maj7 chord, or from the root or 5th of a min7 chord

There are other possibilities for half-diminished, diminished, or dominant chords:
Dominant: Major from root or 6th, dim. from 3rd, minor from 5th
Diminished: Dim. from root, b3, b5, or 6 (bb7)
Half-diminished (min7b5): Dim. from root, minor from b3 or 4, aug. from b5, major from 7.

By altering these, you can get a bunch of patterns that are useful over dominant and diminished.
You can also substitute and extend these, for example:
• Playing the patterns for Db7 will give you altered sounds when applied to G7
• Playing the patterns for Em7 will give you Lydian sounds when applied to Cmaj7
• The patterns for min7b5 work for a min6 chord a m3rd up (use Amin7b5 for Cmin6)

Which brings up another idea, these patterns are all a triad with one added note, a useful concept. Could be another post to come . . .

Friday, December 17, 2010

Here's an (IMHO) excellent exercise that trains your ears and works on connecting your hearing and improvising. I forget where I got the initial idea, but this the the procedure I've developed and found helpful:

Take a chord progression (maybe a blues to start, or just I-vi-ii-V, or an easy standard like Autumn Leaves). Play through the whole chord progression on a chordal instrument, very slowly, while singing the tonic of the key over every chord (even the ones where it doesn't 'fit', even if the apparent key changes).

Repeat, singing the 3rd of the key.
Repeat, singing just 1 and 3.
Repeat, singing the 5th of the key. Then combine 1, 3 and 5. Depending on your range, you may add in octaves of these notes as well.

You may be surprised at this point how much music can be made with just those three notes, and that most chord changes can be negotiated by simply switching to one of the other two notes.

Keep repeating the tune (over several practice sessions), adding in the remaining diatonic tones. I recommend the following order: 6th, 2nd, 7th, and 4th, but feel free to experiment.

When you add a new interval follow the following pattern:
1st chorus: only the new interval {x}
2nd chorus: only 1 + {x}
3rd chorus: only 1, 3, 5 + {x}
4th chorus: all intervals

Once you can do this, again it may seem surprising how much you can play and negotiate changes just using the diatonic notes, by hearing which notes work where and how.

Then you can start adding in chromatic tones. I like to start with the "blues notes": b3, #4, b7. Then eventually add #5 and finally b2 (crunchy!).

In all of the above, I'm talking about the interval in the key, not intervals in relation to each chord.

Once you've done all 12 notes, then you can try going through the progression singing the root of each chord, then the 3rd, 5th, etc.

Note that different keys will put different intervals in different parts of your range. Practicing in different keys is helpful so that sometimes the tonic is in the middle of your range, sometimes at the low end, etc.

Wednesday, August 25, 2010

Update: I linked some parts to my previous posts on Augmented Scale ideas.

Over at the All About Jazz forum, someone asked for suggestions about how to approach Maj7#5 chords. As this is a sound I'm fond of and have spent considerable time exploring, I posted a rather lengthy response.
I'm reprinting part of my response here, since I think it may be of general interest. It's somewhat off the cuff, so the information is probably not optimally organized, so apologies in advance.

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Maj7#5 can take some different sounds, depending on context. Lydian Augmented (third mode of melodic minor) is one of the scales most commonly recommended as being compatible with a Maj7#5 chord. It's not the only one, though, and others might work much better, depending on the context.

Harmonic Major (6th mode) is the same as Melodic Minor #4 (3rd mode) AKA Lydian #2 #5. Just two ways of thinking about it.

What notes will work best over the chord will depend greatly on the harmonic context, e.g. the preceding and following chords, etc.

Try finding some tunes that have the sound in it, substituting it in standards, or writing your own, to experiment with different contexts.

The symmetrical augmented scale is a great sound and can be considered as two augmented triads a 1/2 step apart (contrast with the whole tone scale: two augmented triads a whole step apart). Since augmented chords are symmetrical, any note can be considered the root.

Cmaj7#5: C+/B+ or E+/D#+, or Ab+/G+

You can also extend each triad into a maj7 arpeggio:
Cmaj7, Emaj7, Abmaj7

Since #5 omits the problematic tones, it may be an easier scale to start with: it is less likely to lead to obvious clams.

One could create another 6-note scale that leaves out both P4, A4 and M6:
C D E G Ab B. Such a scale might be useful. It could be viewed as a C+/G triad pair or (perhaps less usefully) as a C/Abdim triad pair.

There are a couple of hexatonic subsets that leave out P4 and M6, but include the A4:
C D E F# G# B: this is C+/Bm, a subset of Lydian Augmented
C D# E F# G# B: This is C+/B, a subset of Lydian Augmented #2

The last one includes a b9 on the chord, but this can be a great sound on a modern tune, especially if the chord lasts for a measure or more. It usually works better in the upper register, where it sounds like an extension.
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So there end up being four primary 7-note scale and one 6-note scale possibilities, and a number of pentatonic and hexatonic choices. Here again are the five primary types:

Not all choices work equally well in all situations.
No warranty is expressed or implied; indiscriminate scale usage may result in clams, tomatoes, or acts of violence. I do not take responsibility for the careless use of the above information.